No one alive today will ever know how important Arnold Schoenberg is, if he is important at all. This will take centuries to figure out. Rolling the dice in a fashion more daring than the cubists, the surrealists or the abstract expressionists, Schoenberg wrote music that literally required listeners to change their way of hearing. He did this first by dismissing tonality, and then by introducing a 12-tone system that made each note in the scale equally important, resulting in compositions that sounded harsh, random and even hideous to those accustomed to conventional notions of melody and harmony.

A century after Pablo Picasso painted Les Demoiselles d'Avignon, the museum-going public has gradually grown accustomed to looking at coarse, non-representational paintings. But the same is not true of music because while the eye can stand anything, the ear cannot. Thus, although Schoenberg is widely viewed as the most daring and innovative composer of the 20th century, his music is infrequently performed. The public hates it, concert promoters loathe it, and musicians, who are usually fairly middle-of-the-road in their tastes, are generally speaking not all that crazy about it. The only people who actually love Schoenberg's music are composers like Pierre Boulez and a few cantankerous critics, but even they could be lying.

Born in Vienna in 1874, Schoenberg started out writing fairly conventional post-Romantic music; his revered Transfigured Night demonstrates that had he wanted to be an admired and even beloved mainstream composer, he could have been.

But Schoenberg was determined to make a total break with the music of the past, and by the time he was in his mid-30s, he was writing compositions that were infinitely more demanding than Stravinsky's revolutionary Rite of Spring.

Impossible to get along with, Schoenberg sabotaged his own career by making ridiculous demands on conductors and soloists and by being condescending and nasty to just about everyone. His music, particularly his morbid opera Erwartung and his eerie song cyle Pierrot Lunaire, resembles Joyce's Finnegans Wake, in that both men tried to drag their audiences to the very precipice of the creative abyss, and found that their audiences were unwilling to follow. As with Joyce, the jury's still out on whether Schoenberg's daring innovations will redefine the way people listen to music, or if his ideas merely inevitably lead to a series of ugly, viscerally repellent sounds. Schoenberg, the most iconoclastic, uncompromising composer in history, died in Los Angeles, California, in 1951. That's irony for you.

T is for Peter Ilych Tchaikovsky

The later 19th century constituted a sort of transcontinental death match in which brilliant composers vied to see who could be the most miserable. Gustav Mahler was as neurotic as they come, literally obsessed with death his entire life. Claude Debussy was unlucky in love, had few friends and hated his physical appearance. Richard Wagner couldn't get along with anyone, even the people who went out of their way to be nice to him. But nobody was ever as persistently down in the dumps as Peter Ilych Tchaikovsky, arguably the biggest crybaby in history.

Tchaikovsky is the Paul McCartney of classical music, an endless font of catchy tunes whose reputation has long suffered because critics find his work a bit sappy. Melodically more gifted than anyone except Mozart, Tchaikovsky wrote one gorgeous composition after the other - The Nutcracker, Swan Lake, Sleeping Beauty, the Serenade for Strings, the Violin Concerto and the First Piano Concerto - but none of it helped dissipate the mood of gloom that engulfed him his entire life. It didn't help that he dedicated his majestic piano concerto to a close friend who then told him that he hated it.

Terrified that the public would find out that he was homosexual, even though just about everybody already knew it, Tchaikovsky burned his way through his money, spent a great deal of time on the road - even though he loathed travelling - and apparently was convinced that his head would one day tumble off his shoulders. He spent a major portion of his adult life receiving financial assistance from a rich woman who attached only one condition to their relationship: that they never actually meet. In the end, she turned out to be just as nutty as he was and cut off the cash.

People who say that they do not like Tchaikovsky's music are reacting more against his dimwitted admirers than against the music itself. While it is true that Tchaikovsky revs up the schmaltz factor in the overplayed violin and piano concertos, which are adored by the millions of concert hall drones who loathe anything written after 1900, his last three symphonies are indisputably magnificent and his ballets are the apotheosis of charm. Apparently, he did not know this, and judged his work rather harshly. Tchaikovsky died after drinking a glass of unboiled water in the middle of a cholera epidemic. He may have drunk the water deliberately. Lots of composers had sad lives, but for unadulterated heartbreak it's hard to top this.